We consider three-dimensional incompressible two-phase flow in a porous medium with fractures. Interaction between the fractures and the rock matrix is taken into account. The location, the geometry and the rock properties of the fractures are considered known (discrete model) and the fractures are modeled as two-dimensional interfaces (reduced model). The fractures and the rock matrix have different rock types. Two-phase flow is modeled using the global pressure formulation. The model is presented and numerical experiments are shown.